Question

Question: The head of a rattlesnake can accelerate at 50 m/s²in striking a victim. If a car could do as well, how long would it take to reach a speed of 100 km from rest?

Short answer

The time required by car to reach the speed of is 0.556 s.

Step-by-step solution

Given data

Acceleration,

Initial velocity,

Final velocity,

: Understanding the kinematic equations Kinematic equations describe the motion of an object with constant acceleration. These equations can be used to determine the various physical quantities.  

The expression for the kinematic equations of motion are given as follows:

$n=v_o+at$ … (i)

Here, v_o is the initial velocity, t is the time, a is the acceleration.

: Determination of the time taken to reach the final speed.

Concert the final velocity from km/h to m/s as,

$$\begin{gathered} v=100\frac{\text{km}}{\text{h}}\times \frac{1000\text{m}}{1\text{km}}\times \frac{1\text{h}}{3600\text{s}} \\ =27.78\text{m}/s \end{gathered}$$

Using equation (i), the time is calculated as follows:

$$\begin{gathered} t=\frac{v-v_0}{a} \\ =\frac{27.78\text{m/s-0m/s}}{50{\text{m/s}}^2} \\ =0.556\text{s} \end{gathered}$$

Thus The time required by car to reach the speed$100\text{km/h}$ is$0.556\text{s}$ .